Question

A ladder is leaning against a wall. The top of the ladder is 9 feet (ft) above the ground. If the bottom of the ladder is moved 3ft farther from the wall, the ladder will be lying flat on the ground, still touching the wall. How long, in feet, is the ladder?

Answer 1

The ladder is 9 feet long.

Step-by-step explanation:

To find the length of the ladder, we can use the concept of similar triangles. When the ladder is standing against the wall, it forms a right triangle with the wall and the ground. When the bottom of the ladder is moved 3ft farther from the wall and the ladder lies flat on the ground, it still forms a right triangle with the wall and the ground, but with a different length for the base. To find the length of the ladder, we can set up a proportion between the two right triangles:

Original length of the base / Original length of the ladder = New length of the base / Length of the ladder

Using this proportion, we can solve for the length of the ladder:

9ft / x = 12ft / (x + 3ft)

Multiplying both sides by x(x + 3ft), we get:

9ft(x + 3ft) = 12ft(x)

Simplifying the equation, we have:

9x + 27ft = 12x

3x = 27ft

x = 9ft

Therefore, the length of the ladder is 9ft.